Multiple Choice
Emily is organizing her closet. She has 15 shirts left to hang but has space in one section for 6 shirts. How many ways could she hang shirts in that section?
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Multiple Choice
A student formed a club at their school. They have 13 members, and need to elect a president, vice president, and treasurer. How many ways are there to fill these officer positions?
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Verified step by step guidance1
Identify the number of positions to be filled: president, vice president, and treasurer. This means there are 3 positions to fill.
Recognize that the order in which these positions are filled matters, as each position is distinct (president, vice president, treasurer). This is a permutation problem.
Determine the number of members available to fill these positions, which is 13.
Use the permutation formula to calculate the number of ways to arrange 13 members into 3 positions. The formula for permutations is: , where n is the total number of items to choose from, and r is the number of items to choose.
Substitute the values into the permutation formula: . Calculate the factorials to find the number of permutations.
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